Cyclic Prefix

Due to the multipath propagation,the OFDM symbol may be interfered by previous OFDM symbol .This phenomenon is called inter symbol interference (ISI).To eliminate the effect of ISI,a guard interval is inserted before the OFDM symbol.This is also one of the reasons and characteristics that OFDM system is robust for multipath fading channel.

Generally,the length of guard interval should be longer than the root-mean-square (RMS) delay spread of the channel so that ISI only damages the information within the guard interval.Figure 2.3-1 shows how the ISI is dealt with by the guard

Interval.

Figure 2.3-1 An example of a subcarrier signal in two-ray multipath channel

The component of guard interval is the duplicate of the last data in an OFDM symbol block,hence it is named Cyclic Prefix (CP).An OFDM frame diagram with CP is plotted in Figure 2.3-2.Since the signal is transmitted over a multipath channel,the

received OFDM siganl may contain the delayed by itself.We would like to

demodulate by FFT operation.However,the result of FFT operation could be exact because of the orthogonality among each subcarrier,like the case in Figure 2.3-3 (a).

Tg

Figure 2.3-3 (a) Two-ray multipath effect without ISI

Figure 2.3-3 (b) Two-ray multipath effect with ISI

Noticing that the component of guard interval can not be inserted with zeros.If we insert zeros within guard interval,then system performance will degrade seriously after DFT operation.This is because there will lose orthogonality between zero information and each component of subcarrier.Hence inserting zero information will introduce inter carrier interference (ICI) during the process of DFT.

The case in Figure 2.3-3 (b) shows that ISI and ICI are introduced.

The channel is modeled as a discrete-time time-invariant system with finite-length

impulse response,ie.：

[ ]

The transmitted OFDM signal is given by

[ ] [ ] [ ] [ ]

and the received OFDM signal without noise is obtained as

[ ] [ ] [ ]

After removing the cyclic prefix,the linear convolution of the useful transmitted signal and the channel response can be regarded as circular convolution (2.3-1).

The time domain channel effect could be transformed into a multiplicative effect when demodulating by DFT at the receiver..It is shown that only simple channel estimation and equalization is needed.

In summary,the cyclic prefixed guard interval not only preserves the mutual orthogonality between subcarriers but also prevents the ISI between adjacent OFDM symbols.

2.4 Time and Frequency Offset

At receiver side,OFDM sysytem must operate the inverse process of the

transmitter side.Hence we have to determine the arrival time of an OFDM symbol’s start point in order to capture the most suitable samples in a window for FFT

operation.Since timing errors may introduce both inter carrier interference(ICI) and inter symbol interference(ISI),the OFDM system that has synchronization problem may dramatically degrade the system performance. Timing offset is defined in Figure 2.4-1 (a) & (b).

offset i

Timing θ

Figure 2.4-1 (a) Timing offset inside CP

1

-offset i

Timing θ Timingoffset θ_i+1 Figure 2.4-1 (b) Timing offset outside CP

In discrete-time baseband model,timing offset can be modeled as an integral delay θ,so the received signal ^y

( )

ⁿ can be easily expressed as x

(

n−θ

)

.If θ is less than the CP length as shown in Figure 2.4-1 (a),the received signal is then given by

( )

n x

[ (

n

)

N

y ^{= −θ}

]

.Because of the circular shift property of DFT,the received signal after DFT ,Y_k, in frequency domain is given by

⎟⎠

⎜ ⎞

⎝

= ⎛ X N

Y_{k k} 2πθ

exp (2.4-1)

It can be easily explained as the follows. The constellation is a phase rotation if timing offset is less than the CP length , as illustrated in Figure 2.4-3.However,if timing offset exceeds the CP length as shown in Figure 2.4-1 (b),then ISI and ICI occur and the system performance degrades seriously , as shown in Figure 2.4-4.

Figure 2.4-2 16 QAM constellation with SNR=25

Figure 2.4-3 Timing offset is less than CP

Figure 2.4-4 Timing offset is larger than CP

The frequency difference of the oscilators in transmitter and receiver will result in the frequency offset,which leads to ICI caused by the loss of orthogonality between subcarriers , as shown in Figure 2.4-5.

f'

Figure 2.4-5 Sampling OFDM siganl with a frequency offset or not

The solid black lines in Figure 2.4-5 show the perfect synchronized position in frequency domain.Sampling at these positions of solid black lines will not introduce ICI and can maintain orthogonality with each subcarrier.If there is frequency offset illustrated by solid red lines,then an offset occurs when comparing with the solid black lines.In the descrete-time baseband model,the effect of frequency offset

between two oscillators in the transmitter and receiver can be modelled as f '

exp ,where ε is the ratio of the real frequency offset to the intercarrier spacing,i.e.

f f

= Δ^'

ε .The received siganl with frequency offset is investigated by [3]

and can be represented as

where the channel effect and the noise term are ignored.

After the DFT operation,we have

( ( ) )

From (2.4.3),we can see that experiences an amplitude reduction and phase shift.

is the ICI term caused by frequency offset.

Xk

Ik

It can be seen in Figure 2.4-6 and 2.4-7 that the constellation is only rotated by a small angele under small frequency offset,but the constellation is distored and can not be distinguished when there is a larger frequency offset.

Figure 2.4-6 The contellation is influenced by a small frequency offset

Figure 2.4-7 The contellation is influenced by a lager frequency offset

Chapter 3

IEEE 802.16e WiMax

Worldwide Interoperability for Microwave Access(WiMax) is the common name associated to IEEE 802.16a/d/e standards.

These standards are issued by the IEEE 802.16 subgroup that originally covered the Wireless Local Loop technologies with radio spectrum from 10 to 66 GHz.

According to the different locations of subscriber station (SS) and to avoid the interference from the other base station on SS,the modulation and coding schemes may be adjusted individually to each subscriber station (SS) on a burst-by-burst basis, as illustrated by Figure 3.

For downlink(DL) transmission,multiple SSs can associate the same downlink burst;

and for uplink(UL) transmission,SS transmits in an given time slot with a specific burst.

Figure 3 Adaptive PHY

3.1 IEEE 802.16

IEEE 802.16 standard is for Line-of-Sight (LOS) applications utilizing 10-66 Ghz spectrum. Although this spectral range has a severe atmospheric attenuation, it is suitable for connections in the operator network between two nodes with high

amounts of bandwidth because many base stations are deployed at elevated positions from the ground. This is not suitable for residential settings because of the

Non-Line-of-Sight (NLOS) characteristics caused by rooftops or trees.

IEEE 802.16a is an amendment for NLOS utilizing 2-11Ghz,which is good for Point-to-Multipoint(PMP) and home application.Orthogonal Frequency Division Multiplexing(OFDM) is adopted for transmission.

IEEE 802.16-2004 revises and replaces 802.16,802.16a,and 802.16REVd. This is the completion of the essential fixed wireless standard.Some operators are already interested in integrating this with the Cellular backhaul.After some political debates,it was decided to support not mobile but fixed wireless and nomadic

communications.Nomadicity is this: Users are attached to the network.After a session completes,they can move to a different network.But the session should be

re-established (possibly including the authentication) from scratch;；it does not have a hand-off mechanism.

IEEE 802.16e is a MAC/PHY enhancement for supporting truly mobile

communications at vehicular speeds.This supports a full hand-off.A user’s session is maintained when he moves around.

3.2 OFDM PHY Specification

3.2.1 Time and Frequency Description of OFDM

The WirelessMAN-OFDM PHY is based on OFDM modulation and designed for NLOS operation in the frequency bands below 11 GHz.

The transmitter energy increases with the length of the guard interval while the

receiver energy remains the same (the cyclic extension is discarded).Thus there is a

On initialization,an SS should search all possible values of CP until it finds the CP being used by the BS.The SS shall use the same CP on the uplink. Once a specific CP duration has been selected by the BS for operation on the downlink, it should not be changed.Changing the CP would force all the SSs to resynchronize to the BS.

Figure 3.2-1 illustrates the time structure of OFDM symbol ,while Figure 3.2-2 gives a frequency description of OFDM signals.

Figure 3.2.1-1 OFDM symbol time structure

Figure 3.2.1-2 OFDM frequency description Data sub-carriers：For data transmission.

Pilot- subcarriers：For various estimation purposes.

Null- subcarriers： No transmission at all, for guard bands, non-active subcarriers and the DC subcarrier.

3.2.2 Parameter Setting

(a) Primitive parameter definitions：

– BW ： This is the nominal channel bandwidth.

– N_used： Number of used subcarriers.

– n：Sampling factor. This parameter, in conjunction with BW and N_used

determines the subcarrier spacing, and the useful symbol time.

– G： This is the ratio of CP time to “useful” time.

(b) Derived parameter definitions ：

– N_FFT：Smallest power of two greater than N_used. – Sampling Frequency：^{Fs = floor}

(

^{n BW⋅} ₈₀₀₀

)

^×8000

– Subcarrier spacing ：Δ =f F N_{s FFT} – Useful symbol time： T_b = Δ 1 f – CP Time： T_g = ⋅G T_b

– OFDM Symbol Time：T_s =T_b+T_g – Sampling time：T N_{b FFT}

(c) Table 3.2.2-1 gives the OFDM Symbol parameters

Parameter Value

u sed F F T

N N _200/256

G 1 4 , 1 8 , 1 16 , 1 32 Frequency offset indices of pilot

carriers –88,–63,–38,–13,13,38,63,88 Frequency offset indices of guard

subcarriers

–128,–127...,–101 (numbers：28) +101,+102,...,127 (numbers：27)

n

For channel bandwidths that are a multiple of

otherwise specified then n = 8/7}

Table 3.2.2-1 OFDM symbol parameters

3.2.3

Randomization of Data

A Pseudo Random Binary Sequence(PRBS) generator is shown in Figure 3.2.3-1 Data randomization is performed on each burst of data on the downlink and uplink.The randomization is performed on each allocation (downlink or

uplink),which means that for each allocation of a data block (subchannels on the frequency domain and OFDM symbols on the time domain) the randomizer shall be used independently.If the amount of data to transmit does not fit exactly the amount of data allocated,padding of 0xFF (“1” only) shall be added to the end of the transmission block for the unused integer bytes. For RS-CC and CC encoded data,,padding will be added to the end of the transmission block, up to the amount of data allocated minus one byte,which shall be reserved for the introduction of a 0x00 tail byte by the FEC.

Figure 3.2.3-1 PRBS generator for data randomization

On the downlink, the randomizer shall be re-initialized at the start of each frame with the sequence: 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0. The randomizer shall not be reset at the start of burst #1. At the start of subsequent bursts,the randomizer shall be

initialized with the vector shown in Figure 3.2.3-2.

Figure 3.2.3-2 OFDM randomizer downlink initialization vector for burst #2...N

On the uplink,the randomizer is initialized with the vector shown in Figure

3.2.3-3.The frame number used for initialization is that of the frame in which the UL map that specifies the uplink burst was transmitted.

Figure 3.2.3-3 OFDM randomizer uplink initialization vector

3.2.4

FEC

A Forward Error-Correction code(FEC),consisting of the concatenation of a

Reed–Solomon outer code and a rate-compatible convolutional inner code, shall be supported on both uplink and downlink. Support of Block Turbo Code(BTC) and Convolutional Turbo Code (CTC) is optional.

The most robust burst profile shall always be used as the coding mode when

requesting access to the network and in the FCH burst.The encoding is performed by first passing the data in block format through the RS encoder and then passing it through a zero-terminating convolutional encoder.

The Reed–Solomon encoding shall be derived from a systematic RS (N = 255, K = 239, T = 8) code.Puncturing patterns and serialization order that shall be used to realize different code rates are defined in Table 3.2.4-2. In the table,“1” means a transmitted bit and “0” denotes a removed bit, whereas X and Y are in reference to Figure 3.2.4-1.

Figure 3.2.4-1 Convolutional encoder of rate 1/2

Table 3.2.4-2 The inner convolutional code with puncturing configuration

Table 3.2-4-3 gives the block sizes and the code rates used for the different modulations and code rates. As 64-QAM is optional for license-exempt bands, the codes for this modulation shall only be implemented if the modulation is

implemented.

Table 3.2.4-3 Mandatory channel coding per modulation

When subchannelization is applied, the FEC shall bypass the RS encoder and use the Overall Coding Rate as indicated in Table 3.2.4-3 as CC Code Rate.The Uncoded Block Size and Coded Block size may be computed by multiplying the values listed in Table 3.2.4-3 by the number of allocated subchannels divided by 16.

In the case of BPSK modulation,the RS encoder should be bypassed.

3.2-5

Interleaving

All encoded data bits shall be interleaved by a block interleaver with a block size corresponding to the number of coded bits per the allocated subchannels per OFDM symbol,Ncbps.Table 3.2-5-1 gives the block size of the Bit Interleaver.

Table 3.2.5-1 Block sizes of the Bit Interleaver

3.2.6 Modulation

After bit interleaving,the data bits are entered serially to the constellation mapper.BPSK,Gray-mapped QPSK,16-QAM,and 64-QAM as shown in Figure 3.2-6-1 shall be supported,whereas the support of 64-QAM is optional for license-exempt bands.The constellations (as shown in Figure 3.2-6-1) shall be normalized by multiplying the constellation point with the indicated factor c to achieve equal average power.For each modulation, b0 denotes the least significant bit (LSB).

Figure 3.2.6-1 BPSK, QPSK,16-QAM,and 64-QAM constellations

The constellation-mapped data shall be subsequently modulated onto all allocated data subcarriers in order of increasing frequency offset index.The first symbol out of the data constellation mapping shall be modulated onto the allocated subcarrier with the lowest frequency offset index.

3.2.7

Pilot Modulation

Pilot subcarriers shall be inserted into each data burst in order to constitute the symbol and they shall be modulated according to their carrier location within the OFDM symbol. The PRBS generator depicted hereafter shall be used to produce a sequence, w .The polynomial for the PRBS generator shall be _k X¹¹+X⁹+ . 1

The value of the pilot modulation for OFDM symbol k is derived from wk. On the downlink ,the index k represents the symbol index relative to the beginning of the downlink subframe. For bursts contained in the STC zone when the FCH-STC is present,index k represents the symbol index relative to the beginning of the STC zone.

In the DL Subchannelization Zone,the index k represents the symbol index relative to the beginning of the burst.On the uplink ,the index k represents the symbol index relative to the beginning of the burst.On both uplink and downlink,the first symbol of the preamble is denoted by k=0.The initialization sequences that shall be used on the downlink and uplink are shown in Figure 3.2-7-1.On the downlink,this shall result in the sequence 11111111111000000000110… where the 3rd 1, i.e.,w2 =1,shall be used in the first OFDM downlink symbol following the frame preamble.For each pilot (indicated by frequency offset index),the BPSK modulation shall be derived as follows

DL: c₋₈₈ =c₋₃₈ =c₆₃ =c₈₈ =1−2w_k and c₋₆₃ =c₋₁₃ =c₁₃ =c₃₈ =1−2w_k UL: c₋₈₈ =c₋₃₈ =c₁₃ =c₃₈ =c₆₃ =c₈₈ =1−2w_k and c₋₆₃ =c₋₁₃ =1−2w_k

Figure 3.2.7-1 PRBS for pilot modulation

3.2.8 Preamble structure

The first preamble in the downlink PHY PDU,as well as the initial ranging preamble,consists of two consecutive OFDM symbols.The first OFDM symbol uses only subcarriers the indices of which are a multiple of 4.As a result, the time domain waveform of the first symbol consists of four repetitions of 64-sample

fragment,preceded by a CP.The second OFDM symbol utilizes only even subcarriers,resulting in time domain structure composed of two repetitions of a 128-sample fragment,preceded by a CP.The time domain structure is exemplified in Figure 3.2-12.This combination of the two OFDM symbols is referred to as the long preamble.

Figure 3.2.8-1 Downlink and network entry preamble structure

The frequency domain sequences for all full-bandwidth preambles are derived from the sequence：

-1-j, -1-j, -1-j, 1+j, 1-j, 1-j}

The frequency domain sequence for the 4 times 64 sequence P4x64 is defined by：

( ) ( ( ) )

mod 4

the factor of 2 equates the Root-Mean-Square (RMS) power with that of the data section.The additional factor of 2 is related to the 3 dB boost.

The frequency domain sequence for the 2 times 128 sequence PEVEN is defined by：

( ) ( ( ) )

mod 2

In the uplink,when the entire 16 subchannels are used,the data preamble,as shown in Figure 3.2.8-2 ,consists of one OFDM symbol utilizing only even subcarriers.The time domain waveform consists of two 128 samples preceded by a CP. The subcarrier values shall be set according to the sequence . This preamble is referred to as the short preamble. This preamble shall be used as burst preamble on the downlink bursts when indicated in the DL-MAP_IE.

PEVEN

Figure 3.2.8-2 P_EVEN time domain structure

3.2.9

Frame Structure

A frame consists of a downlink subframe and an uplink subframe.

(a) Time-Division Duplex(TDD) Frame structure

Figure 3.2.9-1 illustrates an example of OFDM frame structure with TDD.

Downlink

– A downlink subframe consists of only one downlink PHY PDU.

– A downlink PHY PDU starts with a long preamble,which is used for PHY

synchronization.

– The FCH burst is one OFDM symbol long and is transmitted using BPSK rate

1/2 with the mandatory coding scheme.

– Each downlink burst consists of an integer number of OFDM

symbols,carrying MAC messages,i.e., MAC PDUs.

Uplink

– A uplink subframe consists of contention intervals scheduled for initial

ranging and bandwidth request purposes and one or multiple uplink PHY PDUs,each transmitted from a different SS.

– An uplink PHY burst,consists of an integer number of OFDM symbols,carrying MAC messages,i.e., MAC PDUs.

In each TDD frame (see Figure 3.2.9-1),the Tx transition gap(TTG) and Rx transition gap (RTG) shall be inserted between the downlink and uplink subframe and at the end of each frame,respectively,to allow the BS to turn around.

Figure 3.2.9-1 example of OFDM frame structure with TDD

z Frequency-Division Duplex (FDD) Frame structure

Basically,the frame structure of FDD is same with the frame structure of TDD.

Figure 3.2.9-2 illustrates downlink and uplink frame structure of an OFDM system.

Figure 3.2.9-2 (a) OFDM frame structure with FDD for downlink subframe

Figure 3.2.9-2 (b) OFDM frame structure with FDD for uplink subframe

3.3 Simulation Parameter

Table 3.3-1 are the simulation parameters used for each simulation in our study (Chapter 4).

Parameter Value

Used subcarrier(N_used) 200

IFFT/FFT size (N ) 256

CP length(L) 32

Bandwidth(BW) 10MHz(n=57/50)

Sampling Frequency(F ) _s 11.392MHz

Useful symbol time(T_b) 22.472μ sec CP time(T_g) 2.809μ sec(G=1 4)

OFDM symbol time(T_s =T_b +T_g) 25.281μ sec

Modulation QPSK Table 3.3-1 Simulation Parameters

3.4 Channel Model

There is not a formal channel model issured for 802.16e.In this thesis we still simulate in SUI channel but make some modifications for Doppler frequency such that it is suitable for mobile channel.

SUI channel is proposed by Stanford University and has 3 terrain types:

(a) Terrain Type A：The maximum path loss category；hilly terrain with moderate-to-heavy tree density.

(b) Terrain Type B：The intermediate path loss category.

(c) Terrain Type C：The minimum path loss category；mostly flat terrain with light tree densities.

Channel Model Terrain Delay Spread rms (μ sec)

SUI 1 C 0.111

Table 3.4-1 Terrain type for different SUI channel and with its delay spread

SUI3(10MHz) Tap power(dB) Delay samples

Tap1 0 0 Tap2 -5 6 Tap3 -10 12

Table 3.4-2 SUI 3 channel model for BW=10 MHz

SUI2(10MHz) Tap power(dB) Delay samples

Tap1 0 0 Tap2 -12 5 Tap3 -15 13

Table 3.4-3 SUI 2 channel model for BW=10 MHz

Table 3.4-1 illustrates the terrain type for different SUI channels ,while Table 3.4-2 illustrates the SUI3 channel for BW=10MHz.

SUI channel model is used for statistic environment,so it is not suit for mobile environment.For NLOS (Non-Line-Of -Sight) transmission,the operating frequency band is between 2~11GHZ.

If relative velocity between transmitter and receiver is =120 km/hr,we can calculate the Doppler frequency under different operating frequency band.

v

For example：

f ：the carrier frequency 2 GHz c

c ：velocity of light(3 10× ⁸m/s)

α

Figure 3.4-1 the angle between propagation path and direction of vehicle

Hence,for the worst case that is α = ,then 0 f =222.22Hz. _d

Next we substitute the Doppler frequency from the each path of original SUI3 or

Next we substitute the Doppler frequency from the each path of original SUI3 or

在文檔中 符合IEEE802.16e都會區域網路傳輸系統的框同步技術研究 (頁 29-0)